I have consistently heard and read that high aspect ratio propeller blades are more efficient than low aspect ratio blades. Can anyone explain the physics behind this?

Thanks and have a good day!

I am not sure about this but there seems to me to be several different factors -

So efficiency to me starts with the last of these, and works back up the list.

As an example, a propellor for a rubber powered model has low power input and is required to transmit that power very efficiently to move the model. So these props are broad bladed, fairly high pitch, and move a large amount of air quite slowly.

In recent times, there has been a move toward high aspect ratio props particularly for F1B/Wakefield. Prop d/p's of 24x22 are not uncommon. There are photos in a recent magazine of a Russian who is using a 28-26x26-22 variable diameter/variable pitch prop. The blades on these are all narrow at 25-30mm wide at 40-50% halfspan. What has to be remembered is that these props are all driven by comparatively short, high powered motors in a composite tube. Put one into a traditional stick model and the two ends would meet in the middle at half wind.

Move up to the sport diesel power ff/rc assist model and the props are all very similar. Blades are now about 1/2 to 3/4 inches wide, with some taper, and all are turning at about 7k to 12k. And they will move a model along at a suitable pace.

Put the same prop on a Dooling 61 or one of the modern speed or combat glow motors and it would destroy itself and the motor.

A wing of a given area (important - remember same area) is usually going to be a more effective lifter when it is at the highest aspect ratio. Less tip losses involved. The prop is a wing going in a circle (similar to my life at times) so it is bound by the same aerodynamics as the wing. It is creating lift and downwash that oriented as a prop is seen as thrust and propwash.

The difference in velocities at the root compared to the tip causes a shaping also. If there is a desire to keep the prop operating at the same RN through the power region of the motor the tips of the prop will be narrower than the root. This is OK because it works out structurally also. I have a gray 3 bladed 20 inch APC prop that literally goes to a point at the tip. Not the classic shape at all. It seems to work though.

The thing is in airplanes it depends on the power source and mounting which gives lots of compromise and controls the shapes of props used. Rubber motors have a certain torque for winds limit that along with no landing gear requirements give the shapes and big diameters seen today.

A gas motor has a peak power curve at really high rpms. The props absorb energy based on shape,length and chord of the blades. Where the power curve meets the prop curve you have an optimum point for energy transfer. Not the best for either but a compromise. It usually ends up with a lot shorter diameter prop than the rubber power ship and looks like a modern speed ship prop.

In both cases materials available can limit the way the prop is designed and this shows up with thick roots and a low aspect ratio. But with Carbon Fiber tech working for us we are seeing what are really good shapes.

In all cases prop shape is a result of the need for transmission of power to the air and this is most effective when the prop is bigger with a high aspect ratio. Just the same as a wing. You can go to low aspect ratios but lose efficiency.

The other day it was warm enough to get out a electrical fan to add a little air moving around for cooling. As I sat looking at it I realized the fan blades were shaped like my hands and had an aspect ratio of less than one. It lookes like a really fat slow speed boat propeller. This seemed contrary to what we had normally been taught for propeller efficiency. But it has a limiting factor, the RPM by the AC electric motor. So to increase lift and downwash the area is increased as much as possible.

It's not true in general. For any given...

thrust
rpm
airspeed
prop diameter
blade number

...there will be one specific blade area or blade chord which will produce the best efficiency (or equivalently, the least shaft power).

The reason is that the blade CL's are inversely proportional to the blade chord. For the best efficiency you want the best blade airfoil CL/CD, which means the blade CL wants to be "just right" -- not too large or too small, like on a wing. So the blade chord needs to be "just right" as well.

But remember that if you change any of the four parameters listed above, the best blade chord will change as well. They are all inter-related. The following proportionality is approximately correct for low pitch props, where the rotational speed dominates the flight speed:

chord ~ thrust / (blade_num * rpm^2 * dia^3 * CL)

So for example, if you increase the diameter by a factor of 1.1 (10% increase) with all else fixed, the blade chord should shrink by a factor of

1 / 1.1^3 = 0.75

or a 25% reduction. Similarly, if you decrease the rpm by a factor of 0.9 (via a larger pitch, for example), the blade chords want to change by a factor of

1 / 0.9^2 = 1.23

or a 23% increase. Note that a larger pitch should be accompanied by a wider blades, and vice versa.

Mark,

How was that formula derived? It looks like some angular velocity and lift equations.

Ben

Yep. Add up the "lift" (thrust) on the blades going around acting like wings. I should stress that it's a proportionality, not an equation. There are some constants missing, like air density, pi, etc.

Also, with significant pitch, you have to take velocity and force components appropriately. Easily doable, but the end result is no longer a simple proportionality. The zero-pitch limiting case I considered is OK for estimation, and gets the point across.

Mark... I take it you're THE Mark Drela of XFOIL fame?

Glad to see you're an R/C enthusiast in addition to being such an asset to the aviation community at large.

APC's website has some very interesting information regarding how they arrive at their design shape and size. They basically say they use proprietary computer programs (obviously using formulas like Mark Drela is referring to) to determine the optimum blade shape and size. I wouldn't be surprised if this technology is that different from that used to develop ultra quiet submarine propellors for the Navy. I don't think anyone else even comes close to offering the variety of propellor choices that APC offers - they offer multi-bladed, thick and thin, wide or standard, small to large, electric and powered - quite an investment in mold machining! There's an interesting article on their website right now about developing multi-bladed props for military UAVs. In my mind, to a certain extent, quiet equals efficient equals performance. You'll see with APC props they all share a fairly high aspect ratio tapering to a scimitar tip shape - this is what is most efficient and is more and more being duplicated on full size designs - the new 5 bladed props on the new J model C-130 Hercs being a case in point. Not being an aeronautical engineer, I'd love to know whether theres an advantage in regards to acceleration with blades with a lower aspect ratio and a more conventional square or paddle blade tip shape. With our model airplanes fuel efficiency isn't our top priority and "pull" in aerobatic maneuvering is - I can't help but notice however that Bolly and Mezjlik (spelled correctly?) props are fairly similar in shape to APC and they are favored on the big buck large scale aerobatic jobs... Comments?

I think some people use carbon fiber props mainly for the look they procure. I have seen planes with Mezjlik props (heavy) along with carbon fiber spinners (light). Sounds to me like a no sense. Not that carbon props are not good but they sure are heavy compared to wood.